Hydrodynamic Layer Thickness of a Polybase Brush in thePresence of Salt

Robin D. Wesley and Terence Cosgrove*

School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, United Kingdom

Laurie Thompson

Unilever Research, Port Sunlight Laboratory, Quarry Road East, Bebington,The Wirral L63 3JW, United Kingdom

Steven P. Armes, Norman C. Billingham, and Fiona L. Baines

School of Chemistry, Physics and Environmental Science, University of Sussex, Falmer,Brighton, East Sussex BN1 9QJ, United Kingdom

Received September 23, 1999. In Final Form: February 11, 2000

A grafted weak polyelectrolyte brush has been prepared by the incorporation of one block of a diblockcopolymer inside a latex particle. The preformed brush shows a maximum in its hydrodynamic layerthickness radius as a function of added salt. Beyond 0.025 M NaCl, the data can be fitted to the scalingrelationship for the salted-brush regime wherein the layer thickness varies as the inverse cubed root ofthe ionic strength.

IntroductionPolymer brushes have been the focus of a large number

of experimental and theoretical studies.1-6 An interestingcategory of these systems is that in which the brush canbe charged. Recent theoretical work in this area1-3 hasled to a phase diagram in which several distinct regimescan be identified. In this paper we focus on the transitionbetween the so-called osmotic brush and salted brushregimes where the height of the polyelectrolyte layerpasses through a maximum as a function of salt concen-tration. Beyond this transition with increasing salt thelayer thickness will fall monotonically as the chargesbecome progressively screened. A unique system for thesestudies is to prepare a polymer brush at the surface of apolymeric latex particle. This can be achieved by using ablock copolymer that has one block that is compatible andcan be incorporated into a latex particle and one blockthat is not. The system of choice in this study comprisesa hydrophobic block of poly(methyl methacrylate) (PMMA)and a weak polyelectrolyte block, poly(2-(dimethyl-amino)ethyl methacrylate) (DMAEMA). These block co-polymers have been studied in solution,7 at the liquid-air interface8-10 and at the solid-liquid interface.11 In

solution, the polymer forms micelles whose structures aresensitive to both ionic strength and added surfactant.7 Ata hydrophobic solid-water interface, the PMMA is pref-erentially adsorbed and the DMAEMA block solvated.11

Using neutron reflection, the authors found that whenthey increased the pH, the DMAEMA block contractedwhereas the MMA block expanded. At pH 9.5 thepolyelectrolyte layer showed a slight increase with in-creasing salt concentration, but at pH 3 only a monotonicdecrease was found. In this note we describe the variationin the hydrodynamic thickness at ∼pH 7 for a tetheredDMAEMA chain. The pKa of DMAEMA is in the rangefrom 6.612 to 7.311 and we compare the results with scalingpredictions.

Theory

A weak polyelectrolyte does not have a fixed charge;the degree of dissociation of the ionizable groups isdetermined by the external pH. To allow direct comparisonwith the system we have studied experimentally, thetheoretical situation for a polybase is discussed.

An equilibrium exists between the neutral (B) andcharged groups (BH+) of a polybase:

The degree of dissociation, R, which is the fraction ofionizable groups that carry a charge, is given by

* To whom correspondence should be addressed.E-mail: terence.cosgrove@bris.ac.uk. www.chm.bris.ac.uk/pt/polymer/pig.htm.

(1) Israels, R.; Leermakers, F. A. M.; Fleer, G. J. Macromolecules1994, 27, 3087.

(2) Lyatskaya, Y. V.; Leermakers, F. A. M.; Fleer, G. J.; Zhulina, E.B.; Birshtein, T. M. Macromolecules 1995, 28, 3562.

(3) Zhulina, E. B.; Birshtein, T. M.; Borisov, O. V. Macromolecules1995, 28, 1491.

(4) Milner, S. T. Science 1991, 251, 905.(5) Szleifer, I.; Carignano, M. A. Adv. Chem. Phys. 1996, 94, 165.(6) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove,

T.; Vincent, B. Polymers at Interfaces; Chapman and Hall: London,1993.

(7) .Wesley, R. D.; Cosgrove, T.; Thompson, L.; Armes, S. P.;Billingham, N. C.; Baines, F., submitted to Macromolecules.

(8) An, S. W.; Thomas, R. K.; Baines, F. L.; Armes, S. P.; Billingham,N. C.; Penfold, J. J. Phys. Chem. B 1998, 102, 5120.

(9) An, S. W.; Thomas, R. K.; Baines, F. L.; Armes, S. P.; Billingham,N. C.; Penfold, J. Macromolecules 1998, 31, 7877.

(10) An, S. W.; Su, T. J.; Thomas, R. K.; Baines, F. L.; Armes, S. P.;Billingham, N. C.; Penfold, J. J. Phys. Chem. B 1998, 102, 387.

(11) An, S. W.; Thirtle, P. N.; Thomas, R. K.; Baines, F. L.; Armes,S. P.; Billingham, N. C.; Penfold, J. Macromolecules 1999, 32, 2731.

(12) Lee, A. S.; Gast, A. P.; Butun V.; Armes, S. P. Macromolecules1999, 32, 4310.

B + H2O h HO- + BH+

4467Langmuir 2000, 16, 4467-4469

10.1021/la991263d CCC: $19.00 © 2000 American Chemical SocietyPublished on Web 04/14/2000

At high pH, R approaches zero as the equilibrium shiftsto favor B groups. At lower pH, R approaches unity ascharged BH+ groups are favored.

If one end of the polyelectrolyte chain is irreversiblyattached to an interface, a brush is formed, provided thegrafting density is sufficiently high.

If the weak polyelectrolyte brush was dispersed in a(theoretical) zero ionic strength solvent, each charged basegroup will be balanced by an HO- counterion. Overall,the brush must remain electrically neutral so all thecounterions must be contained in the vicinity of the brushas if trapped by an imaginary membrane. This trappingof the HO- counterions inside the brush causes the pHinside the layer to be higher than that in the bulk solution.This high local pH means that the equilibrium betweenuncharged and charged polybase groups will shift in favorof the uncharged groups, making the brush effectivelyneutral. The addition of salt to the system allows thepassage of hydroxyl ions through the imaginary membraneinto the bulk solution, the brush retaining its electricalneutrality by the diffusion of a salt anion back throughthe membrane for each hydroxyl ion that diffuses out.

As HO- ions are released from the brush, the local pHcan now begin to approach that of the bulk solution. Thedegree of dissociation will increase as the salt concentra-tion increases, allowing more protons to diffuse into thebulk. As the degree of dissociation increases, the increasedelectrostatic repulsion leads to a stretching of the brush.

Upon further addition of salt, a point is reached wherethe brush has reached its maximum degree of dissociation.Above this point, the screening of charges within the brushbecomes important, and any further addition of salt causesthe brush to collapse. The height, δ, of a brush, can berelated to the chain length, N, and the grafting density,σ, using the scaling model of Alexander and de Gennes:13,14 δ ∼ Nσ1/3. For a weak polyelectrolyte in the salt brushregime the effective surface density can be replaced byσνeff , where νeff is an effective excluded volume parameterwhich includes both electrostatic and nonelectrostaticcontributions. In the salted brush regime the electrostaticcontribution scales as 1/φs, where φs is the salt concentra-tion. Combining these relations for a fixed brush lengthleads to the relation1 δ ∼ φs

-1/3.

Experimental SectionA diblock copolymer based on poly(methyl methacrylate),

PMMA, and poly(2-(dimethylamino)ethyl methacrylate),PDMAEMA, was prepared by sequential monomer addition[DMAEMA first] using group-transfer polymerization as de-scribed previously.15,16 The copolymer had a total number-averagemolecular weight (Mn), by 1H NMR, of 20 000 g mol-1 and apolydispersity (Mw/Mn) of 1.10 as determined by GPC usingPMMA standards. 1H NMR also indicated that the copolymerhad a DMAEMA content of 69.5 mol %. PDMAEMA can beconsidered to be a weak polybase.

A positively charged PMMA latex was prepared using asurfactant-free emulsion polymerization technique. The PMMAlatex was prepared at a temperature of 80 °C; higher temper-atures were found to cause excess evaporation of the monomer,leading to a low yield of particles. 2,2′-Azobis(2-methyl-pro-pionamidine)dihydrochloride (Acros organics, 98% purity) was

used as the initiator, which leads to the formation of -C(CH3)2-C(NH2)2

+ groups on the surface of the particles. The latex hadan intensity averaged diameter of 112.4 ( 0.6 nm as determinedby photon correlation spectroscopy.

The technique of Dewalt17 was adapted to prepare a graftedpolybase. The positively charged PMMA latex was swollen in asolvent containing 60:40 v/v water:tetrahydrofuran (THF). ThePMMA-PDMAEMA diblock copolymer was added to the swollenlatex dispersion. After being stirred for 72 h, the latex wasdeswollen by dilution with water. The deswelling of the latex isbelieved to trap the PMMA part of the copolymer in the PMMAlatex particles, leading to a grafted layer of PDMAEMA chainsexposed to the solution, as shown in Figure 1.

Most of theTHF was removed by careful rotary evaporationunder vacuum. The aqueous sample was then centrifuged at10 000 rpm for 45 min. The grafted polyelectrolyte was thenredispersed in a minimum amount of water by vigorous shaking.This centrifugation/redispersion process was repeated severaltimes to remove any remaining THF and any other impuritiessuch as ungrafted block copolymer. It is unlikely however thatwithout dialysis that the core latex will revert exactly to itsoriginal unswollen diameter.18

For a series of photon correlation spectroscopy (PCS) mea-surements the grafted polybase was diluted with MilliQ Milliporewater to give a final concentration of ≈100 ppm w/w at neutralpH. The size of the grafted particle was then measured as afunction of added salt concentration.

Results and Discussion

The thickness of the polybase layer can be estimated bydetermining the size of the bare particles before graftingand subtracting this from the total thickness of theparticles and grafted layer. Such an approach assumesthat the particle size is unaltered by the grafting processand as such is likely to give an overestimate of the polybaselayer thickness. Small-angle neutron scattering from thesame system can be used to find the radius of the coreparticle after the grafting procedure, by using contrastvariation. If the DMAEMA layer is contrast-matched withan appropriate D2O/H2O ratio, then the observed scat-tering is dominated by the particle.19 The data gave avalue of 66( 8 nm for the particle radius, which is(13) Alexander, S. J. Physique 1977, 38, 977.

(14) de Gennes, P. G. Macromolecules 1980, 13, 1069.(15) Baines, F. L.; Billingham, N. C.; Armes, S. P. Macromolecules

1996, 29, 3416.(16) Baines, F. L.; Armes, S. P.; Billingham, N. C.; Tuzar, Z.

Macromolecules 1996, 29, 8151.

(17) Dewalt, L. E.; Ou-Yang, H. D.; Dimonie, V. L. J. Appl. Polym.Sci. 1995, 58, 265.

(18) Garreau, L. M. Sc. Thesis, University of Bristol, 1999.(19) Wesley, R. Ph.D. Thesis, University of Bristol, 1999.

R )[BH+]

[B] + [BH+](1)

Figure 1. A schematic representation of the grafted blockcopolymer.

4468 Langmuir, Vol. 16, No. 10, 2000 Wesley et al.

considerably larger than the bare particle. This can beaccounted for by the ingress of the MMA block of thecopolymer and traces of residual THF.

In Figure 2 we show the total hydrodynamic diameterof the core particle and the grafted brush obtained at apH ≈7, at which the DMAEMA chain is ≈50% ionized.12

In the absence of added salt, the total radius was 74.2 nm.Subtracting the postgrafted core particle radius gives ahydrodynamic radius of 8.2 nm. The radius of gyration,RG, of the DMAEMA block can be estimated from light-scattering data20 to be ≈6.8 nm and the extended length64 nm. The layer thickness as calculated is therefore ofthe order of RG.

Figure 2 also shows the total hydrodynamic radius ofthe polyelectrolyte-grafted latex particles as a function ofadded salt. At very low salt concentrations a peak isobserved in the thickness of the grafted polybase, butbeyond 0.025 M NaCl, the layer thickness decreases. Thisregion of the data has been expanded in the insert to thefigure. This observation is in good qualitative agreementwith the idea of a transition from an osmotic brush wherethe layer thickness is increased due to ionization and asalted brush where the charges become progressivelyscreened. The effects seen here are quite dramatic andlarger than the limited data observed at the solid-liquidinterface.11 The hydrodynamic radius is known to depend

strongly on the presence of tails and in a charged brushthe chain segments will be strongly stretched. In theneutron reflection studies referred to above, the thicknessof the diffuse brush layer is not very sensitive to dilutetail segments and hence the observed effects are expectedto be less pronounced. In Figure 3 we have replotted thedata as a function of [NaCl]-1/3 and a clear linear regionis found consistent within experimental error with thescaling prediction derived above. To obtain the linearregion, a bare particle radius must be subtracted, and togive the correct exponent, we require a bare particle radiusof 70 nm, which is consistent with the error bounds of thedata above.

ConclusionsThe influence of salt on the hydrodynamic thickness of

a weak polyelectrolyte brush has been measured. Amaximum has been found in the thickness at intermediatesalt concentrations as has been predicted by theory. Agood agreement with scaling theory in the salted-brushregime has also been found.

Acknowledgment. R.W. and F.B. would like to thankEPSRC, Unilever and Courtaulds for CASE studentships.We also acknowledge NIST for the provision of neutronfacilties and to Tania Slawecki for help in obtaining theexperimental data.

LA991263D(20) Armes, S. P., unpublished data.

Figure 2. Hydrodynamic radius of the grafted particle as afunction of added salt. The inset shows an expansion of thelow-salt region.

Figure 3. Hydrodynamic radius of the grafted particle as afunction of added salt, showing the dependence on [NaCl]-1/3.

Polybase Brush Layer Thickness near Salt Langmuir, Vol. 16, No. 10, 2000 4469